Optimal control of multivalued quasi variational inequalities

Optimal Control of Generalized Quasi-Variational Hemivariational Inequalities and Its Applications

“…The difficult problems are to present the relationships between A and A n , G and G n . Our results extend and improve the results in [10].…”

“…In this work, we study the optimal control of generalized quasi-variational hemivariational inequalities with multivalued mapping which stems from an interesting recent paper by Khan and Sama [10]. In their work, by means of several useful applications, the authors showed the necessity to explore multivalued quasi variational inequalities.…”

An Optimal Control Problem Governed by a Kirchhoff-Type Variational Inequality

“…e study of variational inequalities like (4) with b � 0 and related optimal control problems was proposed by Lions [8][9][10], and this topic has been widely studied by many authors in different aspects (cf. [11][12][13][14][15][16][17][18][19][20][21][22][23]). One of the most important methods is the approximation of the variational inequality by an equation where the maximal monotone operator (in this case, the subdifferential of a Lipschitz function) is approached by a differentiable singlevalue mapping with Moreau-Yosida approximation techniques.…”

A Projection Algorithm for Non-Monotone Variational Inequalities

“…Variational inequalities were introduced in 1966 by Hartman and Stampacchia (see [21]), and have numerous important applications in physics, engineering, economics, and optimization theory (see, e.g., [17,21,24,25] and the references therein). The variational inequality problem for a point-to-set operator T : dom(T ) ⊆ R n ⇒ R n and a nonempty closed and convex set C ⊂ dom(T ), is stated as Find x * ∈ C such that ∃u * ∈ T (x * ), with u * , x − x * ≥ 0, ∀x ∈ C.…”